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We propose and investigate a new nonconforming finite element method for the diffusion equation on general triangular and tetrahedral meshes. We prove that the method results in the condensed system for the Lagrange multipliers with a diagonally dominant M-matrix. We also prove that the proposed method is monotone with respect to the solution function on the interfaces between mesh cells.

Monotone discretizations for diffusion equations on triangular and tetrahedral meshes